If you’re like most people, you probably only use the highest common factor (HCF) and lowest common multiple (LCM) when you’re working with fractions. But these concepts are actually very important in everyday life, especially when it comes to maths and money. In this blog post, we’ll discuss what the full form of HCF and LCM is, and how to use them in real-world situations. Stay tuned!

### Understanding HCF and LCM

Understanding HCF and LCM is important for students studying mathematics and can be very useful in solving mathematical problems.

The Highest Common Factor (HCF) of two or more numbers is the largest number that divides evenly into all of the numbers. For example, the HCF of 24 and 36 is 12.

### Calculation of HCF and LCM

To find the Lowest Common Multiple (LCM) of two or more numbers, you find the smallest number that is a multiple of all of the numbers. For example, the LCM of 12 and 18 is 36.

Both the HCF and LCM can be found using a calculator or by hand. To find the HCF using a calculator, divide the largest number by the smallest number and continue dividing the remainder until you get a remainder of zero. To find the LCM using a calculator, multiply the smallest number by the largest number and continue multiplying the remainder until you get a result of one.

If you are finding the HCF or LCM by hand, there are a few steps you can take to make the process easier.

### To find the HCF

- List the factors of each number
- Find the largest number that is a factor of all of the numbers
- Divide the largest number by the largest number’s factors until you find the HCF

### To find the LCM:

- List the multiples of each number
- Find the smallest number that is a multiple of all of the numbers
- Multiply the smallest number by the smallest number’s multiples until you find the LCM

### Things to remember while finding HCF and LCM

There are a few important things you must remember when finding out LCM and HCF. They are as follows:

- The LCM of two or more numbers is the smallest number that can be evenly divided by all of them
- The HCF of two or more numbers is the largest number that can be evenly divided by all of them
- To find the LCM of two numbers, you need to first find their HCF
- To find the HCF of two numbers, you need to divide them by their LCM

### Division method

This is the most common and easiest way to go about it. However, what if you’re dealing with really large numbers? In such cases, using the division method can be quite tedious and time-consuming.

However, steps involved in the division method are:

- Finding the prime factorization of both numbers
- Determining which factors are common to both numbers and what their greatest common factor is
- Determining the lowest common multiple by multiplying all of the common factors together
- Once you have the prime factorization of both numbers, the next step is to find out which factors are common to both and what their greatest common factor is

For example:

The prime factorization of 24 is:

24 = 23 x 31

The prime factorization of 30 is:

30 = 23 x 31

The common factors are: 23 and 31

The greatest common factor is: 23 x 31 = 93

### Relationship between LCM and HCF

The lowest common multiple (LCM) and the highest common factor (HCF) are two important concepts in mathematics that are related to each other. The LCM is the smallest number that can be divided evenly by all of the numbers in a set, while the HCF is the largest number that can evenly divide all of the numbers in a set. In other words, the LCM is the smallest number that is a multiple of all of the numbers in a set, while the HCF is the largest number that is a factor of all of the numbers in a set.

- HCF x LCM = Product of two given numbers, or
- HCF x LCM = First number multiplied with the second number

### Conclusion

In this blog post, we’ve explored the full form of HCF and LCM. We’ve seen how to calculate these values using a variety of methods, including division methods and prime factorization.